Problem 285 - Intermediate Algebra

Question

In the following exercises, convert each percent to \(a\) decimal. $$ 39.3 \% $$

Step-by-Step Solution

Answer

0.393

Step 1: Understand Percent to Decimal Conversion

A percent represents a part per hundred. To convert a percent to a decimal, divide the percentage value by 100.

Step 2: Perform the Division

Divide 39.3 by 100. This can be done by moving the decimal point two places to the left.

Step 3: Write the Result

When 39.3 is divided by 100, it becomes 0.393. Hence, 39.3% as a decimal is 0.393.

Key Concepts

Percent

A percent (%) is a way to express a number as a fraction of 100. The word itself comes from Latin, meaning 'per hundred.' This means when you see a percent, such as 39.3%, it simply represents 39.3 parts out of 100.

Understanding percent is the first step in converting it to other forms like decimals. Percentages are widely used to express proportions and comparisons in various fields such as finance, statistics, and everyday life.

For example: If 39.3% of the students in a class prefer math, it means 39.3 out of every 100 students in the class prefer math.

Decimal Conversion

Decimal conversion is the process of changing a number from its percent form to its decimal form. This is practical in mathematics and everyday calculations to simplify and work with numbers more easily.

To convert a percent to a decimal, you need to divide the percent value by 100. This can be achieved by shifting the decimal point two places to the left.

For example:

• Convert 39.3% to a decimal: 39.3 ÷ 100
• Move the decimal point two places left: 0.393

So, 39.3% as a decimal is 0.393. This method works for any given percent.

Whether it's 50%, 75.5%, or 0.45%, just divide by 100 or move the decimal point to get the answer.

Division

Division is one of the fundamental operations in mathematics. It involves splitting a number into equal parts.

In the context of percent to decimal conversion, division helps in finding the part per hundred. To convert a percent to a decimal, you divide the percentage value by 100.

Here’s how it looks step-by-step with our example, 39.3%:

• Take 39.3, the numeric value of the percent.
• Divide it by 100.
• The result is 0.393.

This simple division allows you to smoothly transition from the percent form to the decimal form.

Mastering division not only assists in percent to decimal conversion but also in many other mathematical problems. Regular practice makes these operations more intuitive and automatic.